Human hair grows at a rate of about 6.849×10^−4

Question

cm per hour to 2.329×10^−2
cm per hour. The rate depends on gender, genetics, age, and health. Find the difference between the high end and the low end of the range. Express your answer in scientific notation. Do not round your answer.(1 point)

Answer 1

To find the difference between the high end and low end of the hair growth rate, we need to subtract the low end from the high end.

The high end of the rate is: \[ 2.329 \times 10^{-2} , \text{cm per hour} \]

The low end of the rate is: \[ 6.849 \times 10^{-4} , \text{cm per hour} \]

Now, we can perform the subtraction:

1. First, convert \( 2.329 \times 10^{-2} \) to have the same exponent as \( 6.849 \times 10^{-4} \): \[ 2.329 \times 10^{-2} = 2.329 \times 10^{-2} \times \frac{100}{100} = 232.9 \times 10^{-4} \]

2. Now we can subtract: \[ 232.9 \times 10^{-4} - 6.849 \times 10^{-4} = (232.9 - 6.849) \times 10^{-4} = 226.051 \times 10^{-4} \]

3. Now we need to express \( 226.051 \times 10^{-4} \) in scientific notation: \[ 226.051 = 2.26051 \times 10^{2} \]

   So, we have: \[ 226.051 \times 10^{-4} = 2.26051 \times 10^{2} \times 10^{-4} = 2.26051 \times 10^{-2} \]

Thus, the difference between the high end and the low end of the hair growth rate expressed in scientific notation is: \[ \boxed{2.26051 \times 10^{-2}} \]